“Too Cool for School? Signaling and Countersignalling”, 2002 (; backlinks; similar):
In signaling environments ranging from consumption to education, high-quality senders often shun the standard signals that should separate them from lower-quality senders.
We find that allowing for additional, noisy information on sender quality permits equilibria where medium types signal to separate themselves from low types, but high types then choose to not signal, or countersignal. High types not only save costs by relying on the additional information to stochastically separate them from low types, but countersignalling itself is a signal of confidence that separates high types from medium types.
Experimental results confirm that subjects can learn to countersignal.
…Contrary to this standard implication, high types sometimes avoid the signals that should separate them from lower types, while intermediate types often appear the most anxious to send the “right” signals. The nouveau riche flaunt their wealth, but the old rich scorn such gauche displays. Minor officials prove their status with petty displays of authority, while the truly powerful show their strength through gestures of magnanimity. People of average education show off the studied regularity of their script, but the well educated often scribble illegibly. Mediocre students answer a teacher’s easy questions, but the best students are embarrassed to prove their knowledge of trivial points. Acquaintances show their good intentions by politely ignoring one’s flaws, while close friends show intimacy by teasingly highlighting them. People of moderate ability seek formal credentials to impress employers and society, but the talented often downplay their credentials even if they have bothered to obtain them. A person of average reputation defensively refutes accusations against his character, while a highly respected person finds it demeaning to dignify accusations with a response.
…We investigate such countersignalling behavior formally with a model that incorporates extra, noisy information on type into a signaling game.
We find that countersignalling can emerge as part of a standard perfect Bayesian equilibrium in which all players are forming rational beliefs and are acting rationally given these beliefs. Countersignalling is naturally interpreted as a sign of confidence. While signaling proves the sender is not a low type, it can also reveal the sender’s insecurity. Since medium types have good reason to fear that the extra information on type will not differentiate them from low types, they must signal to clearly separate themselves. In contrast, high types can demonstrate by countersignalling that they are confident of not being confused with low types.
This possibility arises because in a countersignalling equilibrium, the sender’s expectation over the receiver’s beliefs about her type depends on both the signal and her type, not just on the signal.